Chapter 3 The Tunnel Diode Oscillator Technique
3.3. Principle and theory of operation of a TDO circuit
Figure 3.2 illustrates the standard electrical diagram of the tunnel diode oscillator circuit used in our experimental setups. All the components are surface mount devices (SMD). The capacitors are ceramic while the resistors are thin film.
The LC tank is made up of capacitor and inductor . The small inductor resistance is
represented by the series resistance . In building our resonators we usually start with the inductor which is chosen based on the sample shape and size as well as the physical property that is to be measured.
Typically we deal with solenoids (5-30 turns) of either cylindrical shape or rectangular cross section with typical values in the µH range. However, a large part of my research has focused on using flat coils in an either open or paired configuration. A more detailed description of the flat inductors used in our setup and the advantages over other geometries will be given in Section 3.5. The material of choice in building the coils is copper so, depending on the inductor geometry, the series resistance of our inductors can be anywhere between a few mΩ to hundreds of ohms.
Figure 3.2 Schematic diagram of a tunnel diode oscillator (TDO) circuit used in our experiments
The capacitor , with typical values ranging from 100 pF to 10 nF, is chosen based on the desired resonant frequency but, most importantly, its value must be in the range required for sustained
oscillations. The impedance matching condition to be met for steady state oscillations will be presented in detail later, however, we will mention that the capacitance value is strongly influenced by the choice of inductor and the tunnel diode used.
All of our TDO circuits use the MBD series germanium tunnel diodes manufactured by Aeroflex Metelics. The measured I-V curves for the four models in the MBD series most commonly used are illustrated in Fig. 3.3 below. It is easy to see that the measured I-V curves deviate considerably from the theoretical behavior suggested in Fig. 3.1 which can pose serious issues when trying to use theoretical models to describe the circuit behavior. Nonetheless, they all exhibit the region of negative differential resistance required for TDO resonance. The negative differential resistance ⁄ is a function of
voltage, however, we can define a total negative resistance ( ) ( ⁄ ) where and are the values of voltage and current at the maximum point of the I-V curve with
and the values at the minimum point in the negative resistance region. The measured values of
for the MBD series are shown in the inset of Fig. 3.3. The impedance of the LC tank dictates the choice of the tunnel diode model. The steady state condition for oscillations is met when the average value per cycle of the power supplied by the tunnel diode equals the power dissipated by the rest of the circuit active components.
The parasitic suppression resistor is used to prevent parasitic oscillation caused by the stray capacitance of the diode or by the inductance of the components. Typical resistance values for in our circuits range from 50 Ω to 300 Ω.
Figure 3.3 I-V curves for 4 models of the MBD series germanium tunnel diodes made by Aeroflex Metelics. Inset: absolute values of average negative resistance for each model
The bypass capacitor value is chosen high enough to appear as a short circuit at the operating frequency value. Its purpose is to close the circuit thus separating the resonant side from the influence of external sources on the frequency (such as capacitance and inductance of the cables) as well as
minimizing external noise. The typical values for the capacitance of in our setups are in the 500-3000 pF range. Although higher values would improve the decoupling from the external environment, the choice of value is limited by the fact that the rfsignal to be measured is extracted from the back of the tunnel diode meaning that high capacitance values of would also drain a considerable amount of the signal to the ground. Consequently, the choice of is a compromise between signal amplitude, external influence and noise.
From the anode terminal of the tunnel diode, the pure rf signal is separated from the dc
component by the coupling capacitor . It acts as a dc block for the signal which is then amplified and ultimately passed to the frequency counter. The high value of the coupling capacitance is in the order of µF although for most of our circuits, a dc block commerical circuit was used.
To push the diode in to the negative resistance region, a bias voltage (0.1-0.5 V) has to be applied to the tunnel diode but since the rf signal is extracted from the terminal of the diode, a constant voltage potential is detrimental. Consequently, a voltage divider made up of resistors and has to be used. The choice of resistance values is largely dictated by the available power supply maximum output voltage although other effects such as resistive heating and power dissipation, source voltage stability and diode characteristics have to be considered. Typically we use high values (order of a few kΩ ) for and an order of magnitude less for (50 Ω-500 Ω) with power supply voltages ranging from 3 to 25 volts. Choosing the value of is important as small values can diminish the rf signal and values larger than the negative resistance of the tunnel diode can result in absence of oscillations.
The capacitor symbolizes the parallel capacitance of the tunnel diode which can be increased by adding a capacitor in parallel with the diode. This optional use of an additional capacitor can enhance the rf signal magnitude in the back of the diode and can also aid in adjusting the impedance of the diode to match the one of the LC tank.
What values for the components will make the circuit oscillate and what are the optimum values? For designing a reliable and precise TDO based experimental technique these are questions have to be addressed. Understanding the principles behind the tunnel diode resonator can greatly aid in the construction of a circuit with superior qualities. A thorough theoretical analysis of the TDO circuit is, despite its relative simplicity, very hard to realize as the electronic components are far from their ideal counterparts. However, a great deal can be understood about generation condition and oscillation frequency of a TDO by making a few assumptions about its constitutive elements.
There are a few studies in literature dealing with the theoretical investigation of the tunnel diode oscillator behavior. C. T. Van Degrift and D. P. Love [148] solved the differential equations system for electronic charge in a simplified version of the circuit and suggested the use of numerical modeling or the
use of an analytical approximation of the tunnel diode I-V curve. They arrived to an approximate expression for the frequency of harmonic oscillations of the form:
√ , ( )- ( 3.1 ) where the form of the function ( ) is given in [148] and
√ ( 3.2 )
is the resonant frequency of an ideal LC circuit.
S. G. Gevorgyan et al. [131] included the influence of the p-n junction capacitance of the tunnel diode as well as its negative resistance value in the calculations and arrived at the following expression for the resonant frequency:
√ *
( ) ( ) + ( 3.3 )
where √ ⁄ , ( ⁄ )√ ⁄ is the quality factor of the LC tank and ⁄ . They also showed that, in order to have sustained oscillations the following generation condition has to be met:
( 3.4 )
Using the quality factor expression, the condition for stable oscillations can be written as: | | √
( 3.5 )
where is the resonance impedance of the LC circuit. We can see that, in order for sustained
oscillations to exist, the impedance of the tank plus the contribution from the parasitic suppression resistance has to be larger than the absolute value of the negative resistance of the tunnel diode. A value of too small, determined by either a large capacitance value or large resistance of the coil, will
result in unbalanced energy losses thus damped oscillations. We can see from Eq. 3.5 that, depending on the component values of the LC tank, the oscillation generation condition can be met if the right tunnel diode type is chosen, based on its negative resistance. As an example, for the MBD series, the BD5 diodes have the smallest , therefore they are best suited for inductors with high resistive losses.
As mentioned before, from a practical perspective, we are interested in the resonant frequency value of the TDO circuit. Frequency measurements are amongst the most precise types available, however frequency counters have a minimum input signal amplitude value requirement. Moreover, if the rf signal magnitude is comparable to external source signals, the frequency value will be distorted by noise effects. It is therefore meaningful to analyze in detail the oscillations amplitude in a TDO circuit. Following the approach in [131] we assume that the oscillations are harmonic with magnitude in the form
. In the steady oscillation mode of the TDO, from energy conservation considerations, the rf energy feeding of the tunnel diode must cancel out the rf energy losses in the circuit. These losses are mainly due to ohmic behavior of the inductor but are also caused by the overall resistive losses in the circuit, as well as by rf radiation. The average energy loss per unit cycle can be written as:
∫ ( ) ( ) ( ) ∫ ( ) ( )
( 3.6 ) where is an effective resistance of the circuit and ⁄ an effective loss conductance.
The average energy feed per unit cycle can be written in a similar form:
( 3.7 ) where is the tunnel diode’s oscillation period averaged differential conductance defined as [131]:
∫
( )
( )
( 3.8 )
The tunnel diode current is dependent on the voltage drop across its terminals which is a sum of the bias voltage and the harmonic voltage . The oscillation condition is met when , therefore the condition in Eq. 3.5 can also be expressed as:
| ( )| ( 3.9 )
From Eq. 3.8 the oscillation amplitude dependence on diode bias voltage ( ) can be derived if the I-V curve analytical expression of the tunnel diode is known. This can be achieved if we consider a polynomial fit for the measured I-V curve of our tunnel diodes. We show in Fig. 3.4 below an example of
( ) curves for 50 different values of voltage bias ( in 50 steps) obtained using Eq. 3.8 by fitting the measured I-V curve of a MBD4 tunnel diode with an 8 degree polynomial function. One can see that a tunnel diode can accommodate a wide range of values and that the oscillation
condition (Eq. 3.9) is satisfied for a large range of bias voltages and oscillation amplitude i.e. any horizontal straight line at vertical coordinate will satisfy Eq. 3.9 within an area delimited by the
( ) curves.
On the right side of Fig. 3.4 we show the calculated oscillation amplitude dependence on the bias voltage ( ) for . It is easy to see that there is an optimum value of for which the oscillations have a maximum amplitude and that, at large enough bias voltage values (240mV in the case depicted in Fig. 3.4), the oscillations will die away. It is important to note that resonance causes the voltage drop on the diode to oscillate over a wide range of values which may include regions on the I-V curve not characterized by a negative differential resistance. However, by changing the bias voltage, the time averaging region can be modified to accommodate the total losses, providing the necessary condition for sustained oscillations.
Figure 3.4 Left: Average period conductance vs. oscillation amplitude ( ) curves for the MDB4 tunnel diode at 50 different values of bias voltage from 90 to 230 mV. Right: oscillations amplitude versus bias voltage ( ) calculated for .
Moreover, although the voltage drop across the LC circuit is harmonic, a large oscillation amplitude means that the voltage across the diode will be nonlinear. For small enough oscillation amplitudes, the negative region on the I-V curve can be approximated with a straight line. In practice, however, large amplitude values are preferred, thus, the measured ac signal from the back of the diode will most likely be non-harmonic in nature. This was observed experimentally in a number of our TDO circuits. Nevertheless, this issue is of less practical concern in our measurements as the frequency counters require only a periodic signal regardless of its shape.
To test the predicted theoretical behavior of the tunnel diode oscillator circuit and to gain additional insight into its features, we also carried out numerical simulations for the TDO using the National Instruments Multisim commercial software [149], a SPICE based simulation environment used for circuit design and testing which provides a simple easy to use interface. The advantage of the software is its ability to simulate electronic circuits of great complexity and, most importantly, the option to use electronic components with realistic characteristics. The simulations confirmed the theoretical
expectations for the TDO circuit performance and provided us with constructive information regarding the design and construction of our circuits. Simulations were carried out for the components of some of our TDO circuits and, as an example, we show the results for one of our circuits in Fig. 3.5 where we illustrate the electronic diagram of the TDO circuit together with numerical values and expected signals at different potential node points on the circuit. The tunnel diode used was MBD4 and its current-voltage
characteristic was simulated using a ABM current source with the I(V) dependence obtained from the 8 degree polynomial fit of the measured I-V curve.
From the numerical results, we notice that the ac current amplitude in the LC tank is in the order of mA (probe 1 in Fig. 3.5). Such high current values are expected considering that the LC tank is a parallel circuit at resonance. This information is particularly useful in estimating the magnetic field amplitude created by the coil and also in figuring the resistive power dissipated by the LC tank, which is essential if the TDO is to be used at low temperatures. As previously mentioned, the measured rf signal (oscilloscope curve on Fig. 3.5) is inharmonic due to the nonlinearity of the I-V curve of the tunnel diode. Also, the signal amplitude is of the order of a few mV at the point where the signal is extracted meaning that the small signal has to be amplified before being forwarded to the frequency counter.
Looking at the resonant frequency expression for a TDO circuit in Eq. 3.3 it is easy to see that it is considerably different than one expected for an ideal LC circuit (Eq. 3.2). Moreover, the expression is obtained considering that the impedance of the bypass capacitor is low enough to act as a short and decouple the circuit from external sources. In practice however, a relatively low capacitance value is needed to extract the rf signal to be measured. This capacitance can also influence the resonance frequency especially if its value is low enough to allow for a significant influence from the connecting cables inductance/capacitance. The obtained numerical results suggest that the influence on resonant frequency of the bypass capacitor is negligible e.g. for the values in the TDO circuit tank of Fig. 3.5 doubling the capacitance value of from 470 pF to 940 pF caused a frequency shift of only 2 kHz (10-5 %).
Ultimately, the resonant frequency of the TDO is dependent upon a large number of factors including all electronic components parameters and even the applied voltage. However, numerical simulations have shown that the major contribution to the deviation from the expected value for an ideal LC circuit (Eq. 3.2) is determined by the capacitance value of the tunnel diode (or the parallel capacitor ). This can also be observed by taking a closer look at the TDO frequency expression in Eq. 3.3. If we consider the component values from the TDO circuit diagram depicted in Fig. 3.5 we expect that ~ ≈ 4.5 kΩ. This suggests small values of which lead to negligible values (~0.5e-3) for the
term linear in and more so for the last term which is quadratic in . Also, ⁄ ≈ 1.5 x 106, which for pF values of , results in a negligible contribution from the 3rd term in Eq. 3.3. The only term of
considerable weight is the 2nd term containing the ratio ⁄ thus, for the diode’s parallel capacitance values comparable to the capacitance of the LC tank, the resonant frequency of the TDO will be
considerably different than that of the ideal value. As an example, for the 10 pF value of the circuit in Fig. 3.5, the resonant frequency is ~ 22.9 MHz. The corresponding ideal LC circuit frequency value would be
≈ 23.7 MHz. The TDO frequency will approach its ideal value if the parallel capacitance of the tunnel diode is considerably less than that of the LC tank. The MBD-E28X series has a relatively small junction capacitance ( ≈ 0.5pF), however, a finite value is required for application purposes considering that the capacitance of the diode provides the necessary means for extracting the rf signal from the LC tank (the measured signal is picked up from the anode terminal of the diode).
In our practical application of the TDO circuit, in order to match the negative resistance of the diode with the impedance of the LC tank, we avoided the use of a large parallel capacitor values with the tunnel diode. We choose a large enough (larger than ) LC tank capacitance and the proper diode to match the tank impedance and also found that the small junction capacitance is sufficient for a
measurable signal in most cases. Consequently, the TDO resonant frequency can be approximated to the value of the ideal LC circuit for most practical applications.